In documents SU-A-1 333 870 and SU-A-943 444, the inventor has described the general principle of an energy-accumulating heterogeneous structure of the type comprising a porous capillary solid matrix that is lyophobic relative to the liquid surrounding said matrix, i.e. the matrix is not wetted by the liquid. Nevertheless, the capillary porosity is defined in theoretical and rudimentary manner in those documents, using capillary passages of constant section. In fact, it turns out that making such a matrix is very expensive, and that the performance of such a heterogeneous structure is limited in terms of the amount of energy that can be accumulated. Also, a matrix of that type turns out to be unsuitable for obtaining significant results when dissipating energy.